We employ advanced physical and mathematical methods to understand the biophysics of complex cellular processes. A major emphasis has been on the biogenesis of coated vesicles involved in clathrin mediated endocytosis (CME) and other intracellular transport processes. CME is the principal pathway for the regulation of receptors, and internalization of certain nutrients and signaling molecules, at the plasma membrane of eukaryotic cells. The early stage of receptor mediated endocytosis involves the formation of transient structures known as clathrin coated pits (CCPs) which, depending on the detailed energetics of protein binding and associated membrane transformations, either mature into clathrin coated vesicles (CCVs) or regress and vanish from the cell surface. The former are referred to as productive CCPs and the latter as abortive CCPs. We have posited a simple model for CCP dynamics and have carried out Monte Carlo simulations to investigate the time development of CCP size and explain the origin of abortive pits and features of their lifetime distribution. By fitting the results of the simulations to experimental data, we have been able to estimate values of the free energy changes involved in formation of the clathrin-associated protein complexes that comprise the coat, and have shown how the binding of cargo might modify the coat parameters and thereby facilitate CCV formation. A paper based on this work currently is being prepared. In a related study, we having been using quartz crystal microbalance-dissipation (QCM-D) instrumentation to investigate the mechanical properties of clathrin triskelia, clathrin coated vesicles (CCVs), and clathrin cages assembled with and without AP180 adaptor proteins (APs). We have also performed atomic force microscopy (AFM) measurements that complement these QCM-D measurements and facilitate interpretation of the QCM-D data. Using these methods, we find the apparent shear moduli of these structures to be approximately one to two orders of magnitude smaller than the Youngs modulus of a triskelion leg. The values of these shear moduli vary strongly with buffer properties and, to a lesser degree, also depend on properties of their substrate support. For example, we find that the shear modulus of CCVs attached to glass surfaces varies from 5 kPa to 12 kPa when buffer pH is changed over the range pH6.2 to pH7.5. This investigation is a continuation of our earlier work to establish the various mechanical properties of clathrin structures, which are important elements in our physical models. Moreover, pH modulation of the nanomechanical properties of clathrin lattices and related protein structures may be an essential aspect of vesicle transformations that are involved in cellular function. A paper based on this work currently is being prepared. A different project, also relating to mechanical aspects of cell response, involves establishing a reliable method for assessing the coupling between substrate properties and the locomotion of eukaryotic cells.. Our emphasis has been on developing collagen-coupled polymer films (e.g., polyacrylamide) whose formation can be controlled by photopolymerization in a quantitative and reproducible fashion. Our scheme uses an ultraviolet (UV) source of spatially-defined intensity to set up rigidity gradients in a film, The efficacy of the procedure has been confirmed by AFM. Our work currently is directed at examining the response of single cells (e.g., durotaxis). However, an extension will focus on understanding the effects of substrate rigidity on the collective movements of mechanically-interacting cells. Such work may have applications in studies of wound healing, cancer metastasis, and normal and aberrant development of embryonic tissues. Finally, model systems have been devised to examine the movement of charged macromolecules through crowded polymer solutions. These have been developed to mimic the diffusion of proteins within the interiors of biological cells. We measure the movement of labeled molecules by Fluorescence Correlation Spectroscopy (FCS). Using a small probe (RNase A) and dextrans that carry different electronic charge, we have shown that transient, charge-mediated binding can retard the movement of proteins to an extent similar to that due to molecular crowding. This work has been published in the Biophysical Journal.